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Belal Ehsan Baaquie - Quantum Computers: Theory and Algorithms

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Belal Ehsan Baaquie Quantum Computers: Theory and Algorithms

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This book presents various theories and algorithms to create a quantum computer. The concept of the classical and quantum computers, and the concept of circuits and gates are reviewed. The example of the Deutsch and the Deutsch-Josca algorithm is discussed to illustrate some key features of quantum computing. The Grover algorithm, considered to be of major milestone of the subject, is discussed in detail to exemplify the techniques used in computer algorithms. The role of quantum superposition (also called quantum parallelism) and of quantum entanglement is discussed in order to understand the key advantages of a quantum over a classical computer.

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Book cover of Quantum Computers Belal Ehsan Baaquie and Leong-Chuan Kwek - photo 1
Book cover of Quantum Computers
Belal Ehsan Baaquie and Leong-Chuan Kwek
Quantum Computers
Theory and Algorithms
Logo of the publisher Belal Ehsan Baaquie Helixtap Technologies - photo 2
Logo of the publisher
Belal Ehsan Baaquie
Helixtap Technologies, Singapore, Singapore
Leong-Chuan Kwek
Centre for Quantum Technologies, National University of Singapore, Singapore, Singapore
ISBN 978-981-19-7516-5 e-ISBN 978-981-19-7517-2
https://doi.org/10.1007/978-981-19-7517-2
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023
This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd.

The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

Quantum theory introduces a fundamentally new framework for thinking about nature and entails a radical break from the paradigm of classical physics. In spite of the fact that the shift of paradigm from classical to quantum mechanics has been ongoing for more than a century, a complete conceptual grasp of quantum mechanics has till today proved elusive. According to leading quantum theorist Richard Feynman, It is safe to say that no one understands quantum mechanics [1].

The idea of quantum computers was pioneered by Yuri Manin (1980) and Richard Feynman (1981) when they discussed simulations that could not be carried out by a classical computerbut only by a quantum computer. Feynman discussed the ideas of quantum gates and quantum computers in [2]. In 1983, David Deutsch made a crucial advance by proposing that the quantum qubit is the natural generalization of the bit of classical computers [3]. The field over the last two decades has seen phenomenal growth, and the development of a practical quantum computer is poised to be game-changing technology of the twenty-first century.

This book is divided into the following four parts. The introduction in Part I gives a more detailed discussion of these four parts.
  1. The topics in Part I have been chosen to introduce non-specialists and newcomers to this field.

  2. Part II discusses in great detail some of the important special cases that illustrate the workings of a quantum algorithm.

  3. Part III discusses relatively more advanced topics as well as some important applications of quantum algorithms.

  4. The last part is a discussions of some of the general features of quantum algorithms.

Hopefully, after reading this book, one can have a rudimentary understanding of quantum algorithms.

References
  1. Feynman RP (2007) The character of physical law. Penguin Books, USA

  2. Feynman RP (2018) Lectures on computation. CRC Press, USA

  3. Deutsch D (1985) Quantum theory, the churchturing principle and the universal quantum computer. Proceedings of the Royal Society

Belal Ehsan Baaquie
Leong-Chuan Kwek
Singapore
Acknowledgments

We would like to acknowledge and express our thanks to many outstanding researchers in the field of quantum computing.

We would like to thank our respective families for their unflagging support and encouragement, without which this book could not have been written.

One of us (BEB) would like to thank George Zweig, Gerald Gerry Neugerbauer, Clifford M. Will, Jon Mathews, Jeffrey E. Mandula, David Mermin, David Ashcroft and Kurt Gottfried for shaping my views on quantum mechanics. He would also like to thank M. Mahmudul Karim, Behzad Mansouri and Frederick H. Willeboordse for many stimulating discussions on computation and algorithms. He had the privilege of having enlightening discussions on quantum mechanics with peerless scholars and visionaries Richard P. Feynman and Kenneth G. Wilson, for which he is eternally indebted to them.

The other author (KLC) would like to thank Luigi Amico, Berge Englert, Jiangfeng Du, Thomas Durt, Artur Ekert, Rosario Fazio, Fan Heng, David Hutchinson, Myungshik Kim, Jose Ignacio Latorre, Aiqun Liu, Christian Miniatura, Bill Munro, C. H. Oh, Xiangbin Wang, Vlatko Vedral, Marek Zukowski and many others for their constant encouragement and advice. He has also benefited a lot from numerous stimulating discussions with many of his current and past students, post-doctoral fellows and group members (A partial list follows: Davit Aghamalyan, Joonwoo Bae, Kishor Bharti, Shaohen Chew, Andy Chia, Keng Wah Choo, Tobias Haug, Masahito Hayashi, Hermanni Heimonen, Mingxia Huo, Alexander Hue, Kelvin Koor, Thiha Kyaw, Elica Kyoseva, Chee Kong Lee, Ying Li, Cao Lin, Jonathan Lau, Wei Luo, Kian Hwee Lim, David A. Herrera-Mart, Dariel Mok, Ewan Munro, Tiong Eng Ng, Wei Nie, Yuan Shen, Harshank Shrotriya, Sivakumar M. Maniam, Sai Vinjanampathy, Lingxiao Wan, Gong Zhang, Hui Zhang, Zisheng Wang, Janus H. Wesenberg and so forth).

Contents
Part I Fundamentals
Part II Quantum Algorithms
Part III Applications
Part IV Summary
About the Authors
Belal Ehsan Baaquie is an adviser to Helixtap Technologies Singapore He is a - photo 3
Belal Ehsan Baaquie
is an adviser to Helixtap Technologies, Singapore. He is a former professor of Finance at INCEIF University, Malaysia, and a former professor of Physics at the National University of Singapore. He has a Bachelor of Science degree from the California Institute of Technology and a PhD from Cornell University in theoretical physics, specializing in quantum field theory. He later developed an interest in finance and economics and started applying quantum mathematics to these fields. He has written four books on quantum finance: Quantum Finance (Cambridge, 2007), Interest Rates and Coupon Bonds in Quantum Finance
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